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Detailed Contents

  1. Preface

  2. I REGRESSION

    1. 1 Simple Linear Regression

      1. 1.1 Deterministic Models

      2. 1.2 Statistical Models

      3. 1.3 Simple Linear Regression Model

      4. 1.4 Least Squares Estimators

      5. 1.5 Properties of Least Squares Estimators

        1. 1.5.1 

          β^0and

          β^1are Unbiased Estimators of β0 and β1

        2. 1.5.2 

          β^0and

          β^1are Linear Combinations of

          Y1,Y2,,Yn 

        3. 1.5.3 Variance–Covariance Matrix of

          β^0and

          β^1 

        4. 1.5.4 Gauss–Markov Theorem

      6. 1.6 Fitted Values and Residuals

      7. 1.7 Estimating the Variance of the Error Terms

      8. 1.8 Sums of Squares

        1. 1.8.1 Partitioning the Total Sum of Squares

        2. 1.8.2 Coefficients of Determination and Correlation

        3. 1.8.3 The ANOVA Table

      9. 1.9 Exercises

    2. 2 Inference in Simple Linear Regression

      1. 2.1 Simple Linear Regression with Normal Error Terms

      2. 2.2 Maximum Likelihood Estimators

      3. 2.3 Inference in Simple Linear Regression

        1. 2.3.1 Inference Concerning σ2

        2. 2.3.2 Inference Concerning β1

        3. 2.3.3 Inference Concerning β0

        4. 2.3.4 Inference Concerning

          E[Yh] 

        5. 2.3.5 Inference Concerning

          Yh 

        6. 2.3.6 Joint Inference Concerning β0 and β1

      4. 2.4 The ANOVA Table

      5. 2.5 Examples

      6. 2.6 Exercises

    3. 3 Topics in Regression

      1. 3.1 Regression Through the Origin

      2. 3.2 Diagnostics

        1. 3.2.1 Leverage

        2. 3.2.2 Influential Points

      3. 3.3 Remedial Procedures

      4. 3.4 Matrix Approach to Simple Linear Regression

      5. 3.5 Multiple Linear Regression

        1. 3.5.1 Categorical Independent Variables

        2. 3.5.2 Interaction Terms

        3. 3.5.3 The ANOVA Table

        4. 3.5.4 Adjusted Coefficient of Determination

        5. 3.5.5 Multicollinearity

        6. 3.5.6 Model Selection

      6. 3.6 Weighted Least Squares

      7. 3.7 Regression Models with Nonlinear Terms

      8. 3.8 Logistic Regression

      9. 3.9 Exercises

  3. II SURVIVAL ANALYSIS

    1. 4 Probability Models in Survival Analysis

      1. 4.1 Lifetime Distribution Representations

        1. 4.1.1 Survivor Function

        2. 4.1.2 Probability Density Function

        3. 4.1.3 Hazard Function

        4. 4.1.4 Cumulative Hazard Function

      2. 4.2 Exponential Distribution

      3. 4.3 Weibull Distribution

      4. 4.4 Other Lifetime Distributions

        1. 4.4.1 Some One-Parameter Lifetime Models

        2. 4.4.2 Some Two-Parameter Lifetime Models

        3. 4.4.3 Some Three-Parameter Lifetime Models

        4. 4.4.4 Some n-Parameter Lifetime Models

        5. 4.4.5 Summary

      5. 4.5 Moment Ratio Diagrams

        1. 4.5.1 Skewness vs. Coefficient of Variation

        2. 4.5.2 Kurtosis vs. Skewness

      6. 4.6 Proportional Hazards Model

      7. 4.7 Exercises

    2. 5 Statistical Methods in Survival Analysis

      1. 5.1 Likelihood Theory

      2. 5.2 Asymptotic Properties

      3. 5.3 Censoring

      4. 5.4 Exponential Distribution

        1. 5.4.1 Complete Data Sets

        2. 5.4.2 Type II Censored Data Sets

        3. 5.4.3 Type I Censored Data Sets

        4. 5.4.4 Randomly Censored Data Sets

      5. 5.5 Weibull Distribution

      6. 5.6 Proportional Hazards Model

        1. 5.6.1 Known Baseline Distribution

        2. 5.6.2 Unknown Baseline Distribution

      7. 5.7 Exercises

    3. 6 Topics in Survival Analysis

      1. 6.1 Nonparametric Methods

        1. 6.1.1 Survivor Function Estimation for Complete Data Sets

        2. 6.1.2 Survivor Function Estimation for Right-Censored Data Sets

        3. 6.1.3 Comparing Two Survivor Functions

      2. 6.2 Competing Risks

        1. 6.2.1 Net Lifetimes

        2. 6.2.2 Crude Lifetimes

        3. 6.2.3 General Case

      3. 6.3 Point Processes

        1. 6.3.1 Poisson Processes

        2. 6.3.2 Renewal Processes

        3. 6.3.3 Nonhomogeneous Poisson Processes

      4. 6.4 Exercises

  4. III TIME SERIES ANALYSIS

    1. 7 Time Series Basics

      1. 7.1 The Big Picture

        1. 7.1.1 What is a Time Series?

        2. 7.1.2 Why Analyze a Time Series?

        3. 7.1.3 Where Does Time Series Analysis Fall in the Modeling Matrix?

        4. 7.1.4 Computing

      2. 7.2 Basic Properties of a Time Series

        1. 7.2.1 Population Autocovariance and Autocorrelation

        2. 7.2.2 Stationarity

        3. 7.2.3 Sample Autocovariance and Autocorrelation

        4. 7.2.4 Population Partial Autocorrelation

        5. 7.2.5 Sample Partial Autocorrelation

        6. 7.2.6 Computing

      3. 7.3 Operations on a Time Series

        1. 7.3.1 Filtering

        2. 7.3.2 Decomposition

        3. 7.3.3 Computing

      4. 7.4 Exercises

    2. 8 Time Series Modeling

      1. 8.1 Probability Models

        1. 8.1.1 General Linear Models

        2. 8.1.2 An Introduction to ARMA Models

      2. 8.2 Statistical Methods

        1. 8.2.1 Parameter Estimation

        2. 8.2.2 Forecasting

        3. 8.2.3 Model Assessment

        4. 8.2.4 Model Selection

      3. 8.3 Exercises

    3. 9 Topics in Time Series Analysis

      1. 9.1 Autoregressive Models

        1. 9.1.1 The AR(1) Model

        2. 9.1.2 The AR(2) Model

        3. 9.1.3 The AR(p) Model

        4. 9.1.4 Computing

      2. 9.2 Moving Average Models

        1. 9.2.1 The MA(1) Model

        2. 9.2.2 The MA(2) Model

        3. 9.2.3 The MA(q) Model

      3. 9.3 ARMA(

        p,q) Models

      4. 9.4 Nonstationary Models

        1. 9.4.1 Removing Trends Via Regression

        2. 9.4.2 ARIMA(p, d, q) Models

      5. 9.5 Spectral Analysis

        1. 9.5.1 The Spectral Density Function

        2. 9.5.2 The Periodogram

      6. 9.6 Exercises

  5. Index